which is traditionally renormalized into a dimensionless parameter \(Z=mV_{B}/\hbar ^2k_F\) , with \(k_F\)  being the Fermi wavevector. The equivalent transmission probability of the N region is \(\tau =1/(1+Z^2)\) . In the short limit, where the length of the junction is much shorter than the superconducting coherence length (\(L\ll \xi \) ), the phase dependence of the Andreev bound state (ABS) spectrum is given by [1]}
\(E_B(\phi )=\Delta \sqrt{1-\tau \sin ^2 (\phi /2)},\) 
